Williamson, RS;
Sahani, M;
Pillow, JW;
(2015)
The Equivalence of Information-Theoretic and Likelihood-Based Methods for Neural Dimensionality Reduction.
PLOS Computational Biology
, 11
(4)
, Article e1004141. 10.1371/journal.pcbi.1004141.
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Abstract
Stimulus dimensionality-reduction methods in neuroscience seek to identify a low-dimensional space of stimulus features that affect a neuron’s probability of spiking. One popular method, known as maximally informative dimensions (MID), uses an information-theoretic quantity known as “single-spike information” to identify this space. Here we examine MID from a model-based perspective. We show that MID is a maximum-likelihood estimator for the parameters of a linear-nonlinear-Poisson (LNP) model, and that the empirical single-spike information corresponds to the normalized log-likelihood under a Poisson model. This equivalence implies that MID does not necessarily find maximally informative stimulus dimensions when spiking is not well described as Poisson. We provide several examples to illustrate this shortcoming, and derive a lower bound on the information lost when spiking is Bernoulli in discrete time bins. To overcome this limitation, we introduce model-based dimensionality reduction methods for neurons with non-Poisson firing statistics, and show that they can be framed equivalently in likelihood-based or information-theoretic terms. Finally, we show how to overcome practical limitations on the number of stimulus dimensions that MID can estimate by constraining the form of the non-parametric nonlinearity in an LNP model. We illustrate these methods with simulations and data from primate visual cortex.
| Type: | Article |
|---|---|
| Title: | The Equivalence of Information-Theoretic and Likelihood-Based Methods for Neural Dimensionality Reduction |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1371/journal.pcbi.1004141 |
| Publisher version: | https://doi.org/10.1371/journal.pcbi.1004141 |
| Language: | English |
| Additional information: | Copyright © 2015 Williamson et al. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited |
| Keywords: | Neurons, Statistical models, Covariance, Entropy, Linear filters, Probability distribution, Macaque, Optimization |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences > Gatsby Computational Neurosci Unit |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10080256 |
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